IMO 1986 LL CHN13

Origin: CHN

Problem

Let N = {1, 2, . . ., n}, n \geq3. To each pair i, j of elements of N, i ̸= j, there is assigned a number fij \in{0, 1} such that fij + fji = 1. Let r(i) =  j̸=i fij and write M = maxi\inN r(i), m = mini\inN r(i). Prove that for any w \inN with r(w) = m there exist u, v \inN such that r(u) = M and fuvfvw = 1.